Treatment of the t mu+D-2 reaction by the methods of quantum reactive scattering - art. no. 052713

We have applied the methods of quantum reactive scattering to the key reson ant reaction in the muoncatalyzed fusion (MCF) cycle that leads to the form ation of a dt mu muonic molecular ion, in which fusion takes place very rap idly. We have calculated reaction probabilities for the resonances that occ ur in t mu+D-2 scattering for incident kinetic energies less than 0.6 eV an d total angular momentum J(tot)=0. To reduce the six-body problem to a thre e-body problem, the motions of the electrons were treated in the Born-Oppen heimer (BO) approximation while those of the muon were treated with a sophi sticated adiabatic approximation. The resulting three-body potential energy surface (PES) was represented by a pairwise additive approximation. The dt mu part of the PES was scaled to allow it to exhibit the correct binding e nergy of the crucial (J,v)=(1,1) state. Scattering calculations were carrie d out using a hyperspherical formulation, and the positions of the resonanc es were found to occur at energies of a few meV greater than if dt mu is as sumed to be a point particle. A comparison of the resonances with the Breit -Wigner formula allowed us to calculate partial widths for back decay, Gamm a(e)(Jtot). Once these are known for all significant J(tot), the rate of fo rmation of dt mu can be determined. This rate, next to the sticking fractio n, is the most important parameter in determining the rate of the entire MC F cycle. We have also carried out a calculation whereby the muon was treate d in a BO formalism and have found significant differences in the final res ults, demonstrating the importance of treating the muon as accurately as po ssible. This work represents a successful ab initio calculation of this rea ction.